Finite Analytic Model for Flow and Transport in Unsaturated Zone

The finite analytic method is employed to solve the vertical, two-dimensional subsurface flow and transport equations in an unsaturated zone. The finite analytic method treats the nonlinear coefficient terms of the governing equations as constants in the element so that linearized partial differential equations can be obtained and solved in each element. The accuracy and limitations of the numerical method are systematically explored. The flow and transport simulations are examined using a one-dimensional laboratory infiltration test and an analytical solution of a two-dimensional subsurface transport problem, respectively. In the advection-dominant, vertical, one-dimensional infiltration problem, nine spatial weighting schemes are proposed to evaluate the averaged unsaturated hydraulic conductivity in a discretized element. Among them, the geometric mean weighting scheme provides the most accurate results as compared with the infiltration data. In verification of the two-dimensional solute transport problem, the nine-node elements are placed in the interior domain, and different layers of five-node elements are placed at the boundaries to investigate if the numerical experiment setup was proper and the algorithm was accurate. The developed numerical model is then applied to an irregular-domain landfill leaching problem to reveal the features of subsurface transport in unsaturated zone. Numerical aspects to be further explored are suggested.